(1) Field of the Invention
The present invention relates to a method to measure (or estimate) the complex frequency-dependent dilatational and shear wavenumbers of a single slab of material subjected to large static compressional forces. More particularly, this invention provides a method to determine complex dilatational wavespeed, complex shear wavespeed, complex Lamé constants, complex Young's modulus, complex shear modulus, and complex Poisson's ratio.
(2) Description of the Prior Art
Measuring the mechanical properties of slab-shaped materials are important because these parameters significantly contribute to the static and dynamic response of structures built with such materials. One characteristic that most elastomeric solids possess is that, when they are subjected to large static forces (or pressure), their rigidity changes. Materials that have one set of mechanical properties at a pressure of one atmosphere can have very different properties when subjected to increased pressure. The ability to determine the pressure dependence of material properties is extremely important for modeling the behavior of systems comprised of these materials.
Resonant techniques have been used to identify and measure longitudinal and shear properties for many years. These methods are based on comparing measured eigenvalues to modeled eigenvalues and calculating the resulting material properties. These methods do not account for static pressure or large compressive forces. Additionally, they typically require long, slender materials to perform the measurement process. Comparison of analytical models to measured frequency response functions are also used to estimate stiffness and loss parameters of a structure. When the analytical model agrees with one or more frequency response functions, the parameters used to calculate the analytical model are considered accurate. If the analytical model is formulated using a numerical method, a comparison of the model to the data can be difficult due to dispersion properties of the materials. These methods do not take into account large compressive forces.
In the prior art, some efforts have been made to measure material properties under large pressures. These methods consist of placing materials in pressurized settings, insonifying them, and then measuring their response. These methods are difficult because they have to be conducted under great atmospheric pressure that can adversely affect the instrumentation. Safety issues can also arise in connection with laboratory testing at extreme pressures. Finally, a mass loaded long thin rod has been studied with respect to the bar wavespeed and corresponding Young's modulus; however, this work does not investigate shear motion.
Accordingly, there is a need for a method of measuring mechanical properties of slab-shaped materials placed under pressure.